Solving the smooth unknotting conjecture in dimension four and its development
| Project/Area Number |
24540082
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
Matumoto Takao 京都大学, 数理解析研究所, 特任教授 (50025467)
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| Co-Investigator(Kenkyū-buntansha) |
鎌田 聖一 大阪市立大学, 大学院理学研究科, 教授 (60254380)
作間 誠 広島大学, 大学院理学研究科, 教授 (30178602)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ２次元結び目 / ２次元ブレイド / ４次元トポロジー / 数学史 / カスプ / チャート図 / マルコフ型定理 / 不変量 / 2次元結び目 / 2次元ブレイド / チャート図の変形 / 4次元トポロジー / ファンカンペン図 / ケーリー図 |
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| Outline of Final Research Achievements |
The smooth unknotting conjecture in dimension four is reduced to the case which is connected by a one-parameter family of braided surfaces with at most one intersection point to the 2-dimensional braid representing an unknot, by assuming our writing Markov type theorem.
Moreover, in this case we do not know that the given knot is trivial yet but we see that its connected sum with the trivial torus knot is diffeomorphic to the trivial torus knot.
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Report
(6 results)
Research Products
(57 results)
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[Book] 微分トポロジー2012
Author(s)
M.. W. ハーシュ、松本堯生（訳）
Total Pages
287
Publisher
丸善出版株式会社
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